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Maxwell weighs 9 pounds 13 ounces, and a source tells the magazine that mom and baby are doing fine.

Simpson also tweeted the news herself, posting, “BABY NEWS!!!” with a link to an announcement on her website saying, “We are so grateful for all of the love, support and prayers we have received. This has been the greatest experience of our lives!!”

TMZ reported Tuesday morning that Simpson arrived at the hospital with her mother, Tina, her sister, Ashlee, and Johnson’s parents.

Simpson, 31, and Johnson, 32, got engaged in November 2010 but were holding off on setting a wedding date until the baby’s arrival.